Prediction of stroke probability occurrence based on fuzzy cognitive maps

Figures & data

Figure 1. A simple FCM with 6 factors.

Table 1. FCM model factors for prediction of ischemic stroke.

Concepts	Type of values
C1: Blood pressure	Four fuzzy values (Low, Medium, High, Very high), Low < 130, Medium 131-150, High 151-170, Very high > 171
C2: Cholesterol	Three fuzzy values (Low, Medium, High) Low < 200, Medium 201-239, High > 240
C3: Blood sugar	Three fuzzy values (Low, Medium, High) Low < 100, Medium 101-120, High > 121
C4: Heart Disease	Two fuzzy values (Yes, No)
C5: Smoking	Two fuzzy values (Yes, No)
C6: BMI	Three fuzzy values (Low, Medium, High)
C7: Risk of Stroke	Three fuzzy values (Low, Medium, High)

Figure 2. Membership functions of output concept (C7).

Figure 3. Sum of the three linguistic variables suggested by neurologists for the concept of blood cholesterol (C₂) and obtaining numerical weights by defuzzification using the centre of area method.

Figure 4. FCM model for predicting the risk of ischemic stroke with numerical values of the initial weights.

Table 2. Initial weights values, $W_{ij}$, proposed by neurologists.

Ci/Cj	C1	C2	C3	C4	C5	C6	C7
C1	0	0	0.20	0.35	0	0	0.45
C2	0	0	0	0.40	0	0	0.35
C3	0	0	0	0.30	0	0	0.30
C4	0	0	0	0	0	0	0.40
C5	0.30	0	0.15	0.35	0	0	0.25
C6	0.20	0	0.25	0.30	0	0	0.20
C7	0	0	0	0	0	0	0

Figure 5. Subsequent values of concepts till convergence without applying NHL algorithm.

Table 3. Values of FCM concepts at 7 iterations.

C1	C2	C3	C4	C5	C6	C7
0.47	0.51	0.13	0	1	0.37	0.1
0.58258	0.55019	0.54594	0.58493	0.59749	0.53647	0.58345
0.58499	0.55412	0.58663	0.6478	0.55873	0.55278	0.66118
0.58442	0.5545	0.5904	0.65398	0.55495	0.55437	0.67095
0.58429	0.55454	0.59073	0.65455	0.55458	0.55453	0.67205
0.58427	0.55454	0.59076	0.6546	0.55455	0.55454	0.67216
0.58427	0.55454	0.59076	0.65461	0.55454	0.55454

Table 4. Updated weight matrix with NHL algorithm for the first example.

Ci/Cj	C1	C2	C3	C4	C5	C6	C7
C1	0	0	0.19	0.34	0	0	0.48
C2	0	0	0	0.38	0	0	0.33
C3	0	0	0	0.28	0	0	0.28
C4	0	0	0	0	0	0	0.43
C5	0.28	0	0.13	0.38	0	0	0.24
C6	0.19	0	0.23	0.28	0	0	0.24
C7	0	0	0	0	0	0	0

Figure 6. Results of output values FCM for all people data after application of NHL.

Table 5. The proposed NHL-FCM method evaluation results in 15 iterations.

	Accuracy	Recognition Rate Low	Recognition Rate Medium	Recognition Rate High
Fold 1	83%	0.5	1	0
Fold 2	100%	1	1	1
Fold 3	100%	0	1	0
Fold 4	100%	1	1	1
Fold 5	100%	0	1	0
Fold 6	83%	0	1	0.75
Fold 7	100%	1	1	1
Fold 8	100%	1	1	1
Fold 9	83%	1	0.8	0
Fold 10	100%	0	1	1
Fold 11	100%	1	1	0
Fold 12	100%	1	1	0
Fold 13	100%	0	1	1
Fold 14	100%	1	1	0
Fold 15	83%	0	1	0.5

Table 6. Comparison of the neurologists’ opinions with proposed model FCM for algorithm last step.

		The proposed model FCM
The mean opinion of neurologists		Low Risk	Medium Risk	High Risk
	Low Risk	0	0	0
	Medium Risk	0	4	0
	High Risk	0	1	1

Recognition rate low = $\frac{0}{0+0+0}=0$, recognition rate medium = $\frac{4}{0+4+0}=1$.

Recognition rate high = $\frac{1}{0+1+1}=0.5$, accuracy percentage = $\frac{0+4+1}{6}=83\mathrm{\%}$.

Table 7. The method evaluation results with the SVM classifier in 15 iterations.

	Accuracy	Recognition Rate Low	Recognition Rate Medium	Recognition Rate Highp
Fold 1	83%	0.5	1	0
Fold 2	83%	1	0.66	1
Fold 3	83%	0	0.83	0
Fold 4	83%	1	0.75	1
Fold 5	83%	0	0.83	0
Fold 6	83%	0	1	0.75
Fold 7	83%	1	0.75	1
Fold 8	83%	0.5	1	1
Fold 9	66%	1	0.6	0
Fold 10	83%	0	0.75	1
Fold 11	100%	1	1	0
Fold 12	83%	1	0.8	0
Fold 13	83%	0	0.8	1
Fold 14	83%	1	0.8	0
Fold 15	66%	0	0.75	0.5

Table 8. The method evaluation results with the KNN classifier in 15 iterations.

	Accuracy	Recognition Rate Low	Recognition Rate Medium	Recognition Rate High
Fold 1	66%	0.5	0.75	0
Fold 2	83%	1	0.66	1
Fold 3	66%	0	0.66	0
Fold 4	83%	1	0.75	1
Fold 5	66%	0	0.66	0
Fold 6	66%	0	0.5	0.75
Fold 7	83%	1	0.75	1
Fold 8	66%	0.5	0.66	1
Fold 9	83%	1	0.8	0
Fold 10	66%	0	0.75	0.5
Fold 11	83%	1	0.8	0
Fold 12	66%	1	0.6	0
Fold 13	83%	0	0.8	1
Fold 14	83%	1	0.8	0
Fold 15	83%	0	1	0.5